Unless its a Chevy Volt. That was a really interesting car in many ways, but they kneecapped fuel efficiency by eating transformer losses twice instead of licensing Toyota patents.

Not just fixed but most engineers design with UL standards so while they advertise maximum output they're all most efficient somewhere around 80% their maximum.

The batteries help the grid because they can maintain a minimum demand the power plants need and compensate for any excess demand that would tax the grid infrastructure.

I've never tested a generator, are they all producing pure sine waves?